A fully-spectral 3D time-domain model for second-order simulation of wavetank experiments. Part A: Formulation, implementation and numerical properties

In this series of two parent papers, we report on the development and validation of a 3D second order numerical wave tank (NWT) model, SWEET. In the present part (A), the fully spectral time domain formulation is described in detail. Among other original aspects, the resulting scheme is based on a resolution achieved by fast Fourier transforms (FFTs) only, leading to very interesting properties in terms of computational efficiency. An extensive verification study of the model accuracy and convergence properties is reported in the context of both local and global quantities. The efficiency and fast-convergence offered by the proposed spectral method allow one to accurately account for the shortest wavelengths in the wavetank, while keeping computational times within affordable limits. The practical capabilities of the model are reported in length in the parent paper [Bonnefoy F, Le Touzé D, Ferrant P. A fully-spectral 3d time-domain model for second-order simulation of wavetank experiments. Part B: Validation, calibration versus experiments and sample applications. Appl Ocean Res 2005 [submitted for publication]], in which various 2D and 3D complex wave system simulations are compared with experiments and detailed analysis, examples given of the use of SWEET in assisting the design of experiments in a physical wavetank, and more validation results provided.